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Analysis of a queueing model for a call center with impatient customers and after-call work. (English) Zbl 1291.60193

The paper under review studies the following model of call centres. Customers arrive in a multiserver Markovian \(M/M/K/J\) queuing system. If all servers are busy, a customer waits in one of the available \(J-K\) waiting places for an exponentially distributed patient time for its service and abandons the system if at the end of the patience time all servers are still busy. If upon arrival of a customer all servers are busy and waiting places occupied, the customer is blocked and leaves the system. If a customer is served, then after the service completion, he/she leaves the system, but the server remains busy for after-call work (ACW) and unattended. An ACW is assumed to be exponentially distributed. The paper under review derives steady state probabilities of the system, and on their basis computes a variety of performance measures that include the blocking probability, waiting probability, mean waiting time, ratio of customers getting service and abandonment, and the fraction of operators, who are serving customers, working on ACW, or being idle in an arbitrary time.

MSC:

60K25 Queueing theory (aspects of probability theory)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B22 Queues and service in operations research